Question
Download Solution PDFयदि Cosec θ + Cot θ = m है, तो \(\rm\frac{m^{2}−1}{m^{2}+1}\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
cosec2θ – cot2θ = 1
गणना:
⇒ cosec θ + cot θ = m ---- (1)
⇒ (cosec θ - cot θ)(cosec θ + cot θ) = 1
⇒ (cosec θ - cot θ) =1/m
⇒ cosec θ - cot θ = 1/m ---- (2)
समीकरण (1) और समीकरण (2) जोड़ने पर, हम प्राप्त करते हैं,
2cosecθ = m + 1/m
cosecθ = (m2 + 1)/2m ...(3)
समीकरण (1) में से (2) को घटाने पर, हम प्राप्त करेंगे
2cotθ = m - 1/m ...(4)
cotθ = (m2 - 1)/2m
⇒ \(\rm\frac{m^{2}−1}{m^{2}+1}\)
उपरोक्त व्यंजक में समीकरण (3) और समीकरण (4) को रखने पर:
⇒ 2mcotθ/2mcosecθ
⇒ cotθ/cosecθ
⇒ cosθ
अतः अभीष्ट मान cosθ है।
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